Dynamically generated hierarchies in games of competition

Barton L. Brown, Hildegard Meyer-Ortmanns, and Michel Pleimling
Phys. Rev. E 99, 062116 – Published 17 June 2019

Abstract

Spatial many-species predator-prey systems have been shown to yield very rich space-time patterns. This observation begs the question whether there exist universal mechanisms for generating this type of emerging complex patterns in nonequilibrium systems. In this work we investigate the possibility of dynamically generated hierarchies in predator-prey systems. We analyze a nine-species model with competing interactions and show that the studied situation results in the spontaneous formation of spirals within spirals. The parameter dependence of these intriguing nested spirals is elucidated. This is achieved through the numerical investigation of various quantities (correlation lengths, densities of empty sites, Fourier analysis of species densities, interface fluctuations) that allows us to gain a rather complete understanding of the spatial arrangements and the temporal evolution of the system. A possible generalization of the interaction scheme yielding dynamically generated hierarchies is discussed. As cyclic interactions occur spontaneously in systems with competing strategies, the mechanism discussed in this work should contribute to our understanding of various social and biological systems.

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  • Received 24 December 2018

DOI:https://doi.org/10.1103/PhysRevE.99.062116

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsPhysics of Living Systems

Authors & Affiliations

Barton L. Brown1,2, Hildegard Meyer-Ortmanns3, and Michel Pleimling1,2,4

  • 1Department of Physics, Virginia Tech, Blacksburg, Virginia 24061-0435, USA
  • 2Center for Soft Matter and Biological Physics, Virginia Tech, Blacksburg, Virginia 24061-0435, USA
  • 3Department of Physics and Earth Sciences, Jacobs University Bremen, 28759 Bremen, Germany
  • 4Academy of Integrated Science, Virginia Tech, Blacksburg, Virginia 24061-0563, USA

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Issue

Vol. 99, Iss. 6 — June 2019

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